48641: Fluid Mechanics SPR University of Technology Sydney

There are a total of eight questions, and a solution worksheet for all the questions must be submitted along with the answer sheet Table (see next page) so that marking is easier for the markers. See the marking rubrics at the end of this page. The solution worksheet file must be compiled into a single 

1. Assignment cover page (student name, ID, email, subject name, etc.)
2. Originality statement signed. You should acknowledge other students or persons who might haven helped or guided you with the assignment.

1. Completed answer-sheet summary immediately after the originality statement.
2. Calculation worksheet. Markings will be done on the completed answer sheet and validated from  the worksheets. Questions and calculation worksheets can be submitted in scanned images of handwritten worksheets converted to PDF files with clear images. Do not waste your precious time typing the worksheet, as no extra marks are given for such efforts.

Important Note

1. Marking will be done directly on the answer sheet (You must submit the answer sheet along withworkings), with answers cross-checked against the calculation worksheet to ensure students have completed the work themselves and not copied from others.

1. The following marking rubrics will be applied to mark the task:
2. Correct answers in the answer sheet (within ±5%) & Correct workings in the worksheet: 100%

1. Wrong answers in the answer sheet & Correct workings in the worksheet: 75%
2. Correct answers in the answer sheet & Wrong workings on the worksheet: 25%
3. Wrong answers in the answer sheet & Wrong workings in the worksheet: 0 marks
4. No working on the worksheet (with correct answer in answer sheet): 0 marks
5. No attempt: 0 marks
6. If a different unit is used but the conversion results in the correct answer, full marks will be given  unless a specific unit is required.

1. If the answer is wrong/different due to the use of different variables (such as fluid properties, say density or viscosity, coefficients, etc.), please check with the solution worksheet provided and see whether the answers closely match the student's answers. If it matches closely, full marks may be awarded.

1. Identical worksheets between students will be considered plagiarism and reported to the subject coordinator immediately.

1. A 1-mark deduction per day will apply for late submissions without approval. Proof of approval must be attached to the submission.

Answer sheet for Problem A (must be filled and attached behind Assignment cover page)

Problems

1. A vertical agitator tank on a chemical plant is being lifted by a service hoist (upward  acceleration), while the contents rotate as a rigid body due to the agitator. Determine the absolute pressure at point A, located on the tank bottom at the wall. Fluid is 20% brine at 20 °C, and the rotational speed is 120 rpm. (1)

1. A storm-water penstock has an inspection triangular cover mounted on an inclined shaft at angle = 45° to the horizontal. The plate is a right triangle of base width b=0.80 m (measured across the slope) and height = 0.90 m (measured along the slope from the upper vertex down to the base). The upper vertex lies = 0.40 m downslope from the free surface. The tank is full of water ( = 1000 kg m⁻³). Find the resultant hydrostatic force on the plate and the line of action (depth of centre of pressure and its position along the plate). (2)

1. A road tanker completely filled with molasses (no ullage) accelerates on level ground. Treat the liquid as static in the truck’s accelerating frame.

Given:

• Fluid: molasses, ρ= 1450 kgm−3
• Tank geometry: length L=12 m, diameter D=3.2 m
• Vehicle acceleration (forward): a_x=3.0 mꢀs−2
• Minimum internal pressure anywhere in the tanker: p_min=90 kPa
• Gravity: g=9.81 mꢀs−2

Tasks:

1. The maximum pressure difference inside the tanker. (1)
2. The location of the maximum pressure and the corresponding absolute pressure. (1)
3. The hydrodynamic drag of a newly designed submarine drone is to be predicted at a cruising speed of 12 knots(/min) in seawater at 15 °C. To test the design, engineers construct a 1:5 scale model of the drone and place it in a towing tank. The temperature of the towing tank water is also maintained at 15 °C. The drag force is measured with a force balance while the model is towed along the tank.

Task:

Determine how fast the engineers should tow the model through the tank to achieve dynamic similarity between the model and the full-scale prototype. (1)

1. At a beverage bottling plant, a vertical clean-in-place (CIP) jet is occasionally used to hold a removable stainless-steel tray (modelled as a flat plate) during washdown. The nozzle issues a coherent water jet vertically upward into ambient air.

Given 

• Fluid: process water, ρ=998 kgm−3
• Circular nozzle diameter: d₀=60 mm
• Jet exit speed at the nozzle: V₀ = 16 m/s
• Gravity: g = 9.81 m/s²

Tasks

1. a) Determine the maximum weight (and mass) of the tray that can be supported at a height h₁=3.0 m above the nozzle. (0.5)

1. b) Repeat for a height h₂=9.0 m above the (0.5)
2. c) Determine the highest elevation h_max at which the jet can still provide any support to a plate (i.e., beyond which the momentum flux at the plate becomes zero). (1)

1. At an open-cut mine, a dust-suppression rotor distributes water across a haul road. Water enters the hub vertically and steadily at a total flow rate of Q=42 L/s. The rotor has two unequal discharge nozzles, each oriented radially outward.

• Nozzle 1 (smaller): diameter d₁=20 mm ⇒ discharge area A₁=3.14 cm²; radial distance from axis r₁=0.60 m.

• Nozzle 2 (larger): diameter d₂=30 mm ⇒ discharge area A₂= 7.07 cm²; radial distance from axis r₂=0.25 m. Assume the rotor and bearings are frictionless, the water density is 1000 kg/m³, the discharge to the atmosphere, and the mechanical and hydraulic losses are negligible. Flow divides between the nozzles in proportion to their areas.

Tasks

1. a) If the rotor is allowed to spin freely, determine the steady rotational speed n (in rpm) at which the net driving moment from the jets becomes zero. (1)

1. b) If the rotor is held stationary, determine the external torque (magnitude and direction) that must be applied at the shaft to restrain rotation under these conditions. (1)

1. A run-of-river hydraulic turbine–generator is installed in a penstock. Because of screens and bends upstream/downstream, the velocity profiles at the turbine inlet and outlet are highly non-uniform, so kinetic energy correction factors are not negligible.

Given

1. Fluid: water at 20℃ ( = 1000 kg m⁻³)
2. Volumetric flow rate: = 0.73 m³/s (IGNORE IT,
3. Inlet pipe diameter: D₁= 0.40 m (Ignore it, USE 0.4 cm)
4. Outlet pipe diameter: D₂= 0.28 m (Ignore it, USE 0.28 cm)
5. Manometer reading across the turbine casing: differential height of mercury Δℎ = 1.30 m (take _Hg = 13600 kg m⁻³); taps are at the same elevation.

1. Kinetic energy correction factors: ₁ = 1.20 at the inlet, ₂ = 1.05 at the outlet.
2. Combined turbine–generator efficiency: = 0.86 (ignore it, use 0.65)
3. Neglect pipe losses outside the turbine, elevation change between taps, and shaf bearings losses (already included in ).

Tasks

1. Using the extended Bernoulli/energy equation that includes α, determine the shaft power extracted by the turbine (hydraulic power removed from the flow). (1)

1. Determine the net electric power output of the generator. (1)
2. If the generator rotates at = 300 rpm, compute the corresponding shaft torque delivered to the generator. (1)

1. A high-speed process pump uses a sleeve (journal) bearing on the drive end. During a cold start, the lube oil is at 20 °C, and after warm-up the bearing runs at an oil bulk temperature of 80 °C. The bearing is 0.55 m long; the shaft outside diameter is 80 mm; the average radial lubricant film thickness (mean clearance) is 0.80 mm. The shaft is driven at 2000 rpm.

The lubricant is Newtonian with dynamic viscosity

• 0.10 Pa·s at 20 °C (cold start), and
• 0.008 Pa·s at 80 °C (steady operation).

Tasks.

Assuming a concentric shaft (no eccentricity), fully flooded bearing, and negligible end effects, determine the viscous friction torque required to overcome bearing drag (a) at cold start and (b) at steady operation. Provide answers in N.m. (1+1)

Assessment brief what you must submit 

This assessment is a multi-question problem set requiring a completed answer sheet plus a calculation/workings worksheet for each problem. Submit one compiled PDF containing:

• Assignment cover page (name, student ID, email, subject/unit, tutor, word/page count as required)

• Signed originality statement (acknowledge anyone who assisted you)

• Completed answer-sheet summary (one page immediately after the originality statement) this is where markers will record marks

• Calculation worksheet(s) scanned, legible images of handwritten workings converted into PDF (one file). Do not waste time typing the worksheet; scanned handwritten work is acceptable and expected.

• Any Excel files, figures or supporting plots may be attached as separate files if permitted.

Key marking rules you must know (rubric highlights)

• Full marks (100%) only if answer sheet is correct (±5%) and workings on worksheet are correct.

• If workings are correct but your answer sheet differs → 75% (marker will score based on evidence of correct process).

• If answer sheet shows correct number but worksheet lacks correct workings → 25% (penalised heavily).

• No workings shown → 0 marks even if answer is correct.

• Identical worksheets between students = treated as plagiarism.

• Late submissions without approval = −1 mark per day.

Primary expectations for each problem

• Show all assumptions, relevant equations, units and conversions.

• Provide clear, labelled sketches where geometry/pressure distributions matter.

• Use consistent SI units and quote final answers with correct units and reasonable significant figures.

• Cross-check answers (sanity checks) and annotate if alternative units/variables were used.

How the Academic Mentor guided the student 

The mentor structured the support to match the rubric and to teach transferable problem-solving skills rather than just delivering answers.

1. Kick-off: read the brief & plan

   • Reviewed the overall submission requirements (cover page, originality statement, compiled PDF).

   • Created a submission checklist tied to the rubric (workings pages, scanned quality, units, labelled diagrams).

   • Advised dividing the eight problems across a timeline and allocating time per question.

2. Interpret each problem: identify physics & assumptions

   • For each problem the mentor asked the student to state in one sentence the physical principle involved (e.g., hydrostatics with rotating fluid; hydrostatic force on an inclined plate; accelerating frame pressure distribution; dynamic similarity and Froude vs Reynolds; jet momentum support; reaction torques from tangential jets; Bernoulli with kinetic-energy correction; viscous torque in journal bearings).

   • Guided the student to list explicit assumptions (incompressible Newtonian fluid, rigid body rotation, negligible air resistance, uniform density, steady flow in accelerating frame, frictionless bearings where stated).

3. Select equations & solution strategy

   • Mapped each problem to the governing equations and solution strategy: hydrostatic pressure distribution (including rotating frame: p=p0+ρgz+12ρω2r2p = p_0 + \rho g z + \tfrac{1}{2}\rho\omega^2 r^2p=p0+ρgz+21ρω2r2), triangular plate resultant formulae, accelerating-frame pressure gradients, scaling laws for model testing (identify similarity parameter typically Reynolds or Froude depending on flow regime), momentum flux for jets, conservation of angular momentum for jet-driven rotors, extended Bernoulli including α (kinetic energy correction), journal bearing viscous torque formula (Couette/Poiseuille combined approximations).

   • Emphasised writing the full equation, then simplifying with stated values.

4. Workings practice & presentation

   • Taught how to write clear, stepwise workings: statement → equation → substitution → numerical result → units.

   • Recommended using Excel for repetitive arithmetic (tables, unit conversions, parametric checks) and to produce neat numerical outputs that can be pasted as images into the worksheet.

   • Advised to hand-sketch diagrams but compute numerically in Excel to avoid transcription errors; then scan the handwritten worksheet and attach the Excel file.

5. Sanity checks & error handling

   • For each result the mentor encouraged a quick plausibility test (e.g., is the pressure magnitude reasonable given density and height? Is break-even number of guests sensible? Does torque sign match sense of rotation?).

   • If multiple solution methods exist, show the preferred one and note an alternative check with brief justification.

6. Academic integrity & submission polishing

   • Reminded students to sign the originality statement and to acknowledge any help (tutor hints, peer discussion).

   • Checked scanned images for legibility (contrast, orientation) and combined PDFs in the required order.

   • Ran a final checklist: units, labelled axes on graphs, all worksheets present, answer sheet filled and matched to workings.

Final outcome what the student produced

• A single compiled PDF containing: cover page, signed originality statement, completed answer sheet, and clear scanned handwritten calculation worksheets for all eight problems.

• Excel supporting files submitted (used for numeric evaluation, charts and parameter checks).

• Each problem included: a concise problem-statement, governing equation(s), substitutions with units, and final answers marked on the answer sheet within ±5% tolerance.

• Supporting sketches/diagrams for geometry problems and annotated explanations of assumptions.

Learning objectives covered

By completing this assessment under mentor guidance the student demonstrated and developed:

• Applied technical competence applying hydrostatics, rotating flows, accelerating frames, jet momentum, dynamic similarity and viscous bearing theory to engineering problems.

• Analytical problem solving selecting appropriate models, simplifying assumptions, and solution paths.

• Numerical proficiency & tools using Excel for calculation, unit management, and sensitivity checks.

• Professional scientific communication presenting stepwise workings, labelling diagrams, and preparing submission-ready PDFs.

• Academic integrity understanding rubric implications, importance of showing workings, and documenting assistance to avoid plagiarism.

• Quality assurance  performing sanity checks and documenting assumptions and units for marker transparency.

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